A Concise Introduction to Pure Mathematics, Second Edition

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CRC Press, Nov 2, 2005 - Mathematics - 224 pages
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A Concise Introduction to Pure Mathematics, Second Edition provides a robust bridge between high school and university mathematics, expanding upon basic topics in ways that will interest first-year students in mathematics and related fields and stimulate further study. Divided into 22 short chapters, this textbook offers a selection of exercises ranging from routine calculations to quite challenging problems.

The author discusses real and complex numbers and explains how these concepts are applied in solving natural problems. He introduces topics in analysis, geometry, number theory, and combinatorics.

What's New in the Second Edition:
  • Contains extra material concerning prime numbers, forming the basis for data encryption
  • Explores "Secret Codes" - one of today's most spectacular applications of pure mathematics
  • Discusses Permutations and their importance in many topics in discrete mathematics

    The textbook allows for the design of courses with various points of emphasis, because it can be divided into four fairly independent sections related to: an introduction to number systems and analysis; theory of the integers; an introduction to discrete mathematics; and functions, relations, and countability.
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    Contents

    Preface jd 1 Sets and Proofs
    1
    Number Systems
    13
    Decimals
    21
    Inequalities
    27
    n1 Roots and Rational Powers
    31
    Complex Numbers
    35
    Polynomial Equations
    47
    Induction
    57
    Congruence of Integers
    111
    More on Congruence
    121
    Secret Codes
    131
    Counting and Choosing
    137
    More on Sets
    149
    Equivalence Relations
    157
    Functions
    163
    Permutations
    173

    Eulers Formula and Platonic Solids
    71
    Introduction to Analysis
    81
    The Integers
    91
    Prime Factorization
    99
    More on Prime Numbers
    107
    Infinity
    187
    Further Reading
    197
    Index of Symbols
    199
    Index
    201
    Copyright

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